A natural domain decomposition method with non-matching grids

In this paper a natural domain decomposition method based on local Dirichlet-Neumann maps is considered. The global variational problem is defined on the skeleton of the domain decomposition only. For the approximation of the Dirichlet-Neumann maps Dirichlet boundary value problems need to be solved locally. The local finite element spaces within the subdomains can be chosen independently of the global trial space on the skeleton. In particular, this approach can be used to couple non-matching triangulations across the interfaces without an additional framework such as introducing Lagrange multipliers. Numerical results for two model problems confirm the stability and error estimates given here.